## LOCAL

Most events in GeoNet's catalogue from 1942 to 1986 were determined using the LOCAL technique.

For events located before January 1987 with an evaluationmethod of LOCAL, earthquake origins were determined using the phases P, Pn, P, Pg, and the corresponding S phases, in conjunction with a one-dimensional model of the crust shown in the table (earthmodel* nz1d). The New Zealand Standard model was used to calculate travel-times of rays passing through and immediately beneath the crust, except for two regions of special study which featured denser seismograph networks (Wellington network from 1978, Pukaki network 1975 to 1983 only). A provisional origin chosen by an earthquake analyst was repeatedly adjusted to obtain the best agreement between observed arrival times for the various phases, and times computed from tables. More precisely, the origin was adjusted to minimise the sum of the squares of the weighted residuals (originerror) (observed minus computed arrival times).

In general, all four coordinates of the earthquake origin were calculated (origin time, latitude, longitude, and focal depth). In some cases, however, the focal depth was not allowed to vary, but restricted to some chosen depth. This was most commonly done for crustal earthquakes. Unless there was a station within 25 km of a shock in the upper crust, or within 50 km of a shock in the lower crust, a nominal depth of either 12 or 33 km was usually assigned, according to the crustal phases present and the goodness of fit of the resulting solution. The parameter depthtype indicates if there was a restriction for any of the foregoing reasons.

In routine origin determinations, sufficient of the stations nearest to the epicentre were read to yield a satisfactory solution, together with a selection of other stations from which readings were recorded but not used. If enough observations were available, arrival times recorded at stations more than 3° from the epicentre were excluded from the calculations.

Origins determined from the Wellington and Pukaki network data were obtained using a modified technique with different convergence criteria, in conjunction with the velocity models more appropriate for the two areas, shown in the accompanying table.

The parameters usedphasecount and usedstationcount indicate the degree of constraint on the adopted origin: that is, usedphasecount phases from usedstationcount stations were used in the determination of the origin. (All phases given non-zero weight are counted but stations which failed to provide such a phase are not). minimumdistance is the distance from the epicentre to the nearest of these usedstationcount stations, and azimuthalgap is the greatest angular gap in their distribution about the epicentre.

In using the earthquake catalogue, it is essential to keep in mind that the positions of earthquakes with epicentres outside the network of seismograph stations can be very uncertain, even though the originerror is small.

### Magnitudes

The magnitudes assigned to local earthquakes are intended to be the values of ML as originally defined by C.F. Richter (Bull. Seism. Soc. Am. 25: 1-32, 1935), but his procedure for performing the magnitude calculation at other than the standard distance of 100 km was modified, to take account of the observed characteristics of energy propagation in New Zealand, including the effect of focal depth (Haines, A.J., Bull. Seism. Soc. Am. 71: 275-94, 1981).

Magnitudes were based on the largest amplitudes in the P and S phase groups. An amplitude-distance relationship of the form:

$$A = A_o R^{-N} exp( - αR )$$

where $$A$$ is a trace amplitude recorded at an epicentral distance $$R$$, $$A_o$$ is a calibration function, $$N$$ is a geometric spreading factor and α is an inelastic attenuation coefficient, was found appropriate for all parts of the country.

For all New Zealand crustal earthquakes $$N$$ is 2 and $$α$$ generally takes a value close to 0. With these values, the relationship describes head-wave propagation with no attenuation. In the Central Volcanic Region, however, α takes values of 0.8 deg$$^{-1}$$ for P waves and 1.05 deg$$^{-1}$$ for S waves. Adjustments are therefore made according to the distance travelled in the volcanic region.

For deep earthquakes in the Main Seismic Region the same parameters as for crustal earthquakes apply (i.e. $$N = 2, α = 0$$), provided that (i) $$R$$ now measures the slant distance from the focus to the base of the crust, and (ii) stations to the west of the Volcanic Region or south of the Main Seismic Region (south of a line between Cape Foulwind and Amberley) are not used, because the structure demands different spreading and attenuation terms there.

For deep earthquakes in Fiordland the same amplitude-distance relationship is used, with (i) $$N$$ given the value 1 (i.e. body wave propagation), (ii) $$α$$ increasing with focal depth, and (iii) stations in the Main Seismic Region (apart from station COB) not used, because of variations of the coefficients $$N$$ and $$α$$.

Corrections were applied to allow for station characteristics. These include the differences in site effects, frequency response and magnification of the instruments. They were determined empirically in such a manner as to give the most consistent estimates of magnitude from the different stations, and their absolute level was adjusted to give a standard Wood-Anderson instrument at Wellington a zero correction. Station corrections were added to the individual estimates of magnitude, which were then averaged.

The Pukaki network used a formula developed by Eaton (Open File Report, U.S. Geological Survey, 1970) which was modified for consistency among stations and calibrated against available stations of the national network using a few selected shocks.

The Wellington network used both the maximum amplitude and the duration of the signal. Both scales were calibrated against the Wood-Anderson determination at Wellington, for a selection of shocks that were large enough to record there. The formulae are:

$$M_T = -0.81+2.3log_{10}T_i+C_i$$
$$M_A = log_{10}A_i - 1.71+1.56log_{10}R_i + K_i$$

where Ti is the duration in seconds at station $$i$$, $$A_i$$ is the amplitude (mm), $$R_i$$ is the slant distance from the focus (km), and $$C_i$$ and $$K_i$$ are the station corrections for determinations from durations and amplitudes respectively. Individual estimates of magnitude are averaged to give the final values. The number of magnitude estimates contributing to this mean value, and an indication of their scatter, are provided (parameters magnitudestationcount and magnitudeuncertainty).

### Velocity Models

Model (nz1d) Upper Depth Boundary (km) Vp (km/s) Vs (km/s)
New Zealand Standard 0.0 5.5 3.3
12.0 6.5 3.7
33.0 8.1 4.6
Wellington 0.0 4.40 2.54
0.4 5.63 3.16
5.0 5.77 3.49
15.0 6.39 3.50
25.0 6.79 3.92
35.0 8.07 4.80
45.0 8.77 4.86
Pukaki 0.0 4.44 2.60
1.7 5.88 3.44
9.6 6.50 3.80
32.0 8.10 4.70